Prikaz in tolmačenje modelov nenegativne matrične faktorizacije

Gomišček, Rok (author), Curk, Tomaž (mentor)

Atributi, s katerimi opisujemo primere v bazah podatkov, so pogosto zelo številni. Določanje resnično pomembnih atributov za klasifikacijo ter njihovih medsebojnih odvisnosti zato predstavlja velik izziv. Eden od načinov, kako zmanjšati dimenzionalnost prostora in določiti pomembne atribute in primere, je z uporabo nenegativne matrične faktorizacije. V magistrski nalogi smo najprej preučili osnove nenegativne matrične faktorizacije in nekaj načinov prikaza podatkov in faktorskih modelov v matrikah. Predlagamo nekaj načinov, kako prikazati in razumeti modele, pridobljene s faktorizacijo. Uspeh metod smo ovrednotili na nekaj podatkovnih zbirkah in ugotovili, da nam vsaka metoda razkrije uporabne informacije o modelu. Z gručenjem faktoriziranih matrik lahko dobimo čistejše gruče kot z gručenjem izvornih podatkov. S projekcijo primerov v prostor faktorjev lahko ugotovimo, kateri faktorji vplivajo na določene razrede. Če pa tej projekciji dodamo še atribute, lahko sklepamo še o povezavi med primeri in atributi izvornega prostora.

• Language: Slovenian
• Keywords: nenegativna matrična faktorizacija, faktorski model, vizualizacija podatkov
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FRI - Faculty of Computer and Information Science
• Publisher: [R. Gomišček]
• Year: 2015
• Number of pages: 68 str.
• PID: 20.500.12556/RUL-72630
• COBISS.SI-ID: 1536577987
• Publication date in RUL: 29.09.2015

Secondary language

• Language: English
• Title: Visualization and interpretation of models obtained with non-negative matrix factorization

Abstract

Attributes that describe data in the databases present themselves in large numbers. For this reason defining truly important attributes for classification and establishing their mutual dependence poses a significant challenge. One way of reducing the dimensionality of the space and defining important attributes and examples is by using non-negative matrix factorization. In this master thesis we first examined the basics of non-negative matrix factorization and a few ways of visualizing the data and factor models in matrices. We propose a few ways of presenting and understanding the models acquired with factorization. We evaluated the effectiveness of the methods on several databases and learnt that each method reveals useful information about a model. Clustering of the factorized matrices can produce purer clusters than clustering of the source data. By projecting examples to the factor space we can see which factors affect certain classes. Adding attributes to this projection makes it possible to deduce the link between the examples and the attributes of the source space.

• Keywords: non-negative matrix factorization, factor model, data visualization